Analytic Geometry Answers

Find the equation of the line which is perpendicular to 4𝑦=5𝑥−8 and passing through (2,3).

𝐴(1,−2) is a point on the circle (𝑥−3)2+ (𝑦+1)2= 5

a. State the coordinates of the centre of the circle and hence find the coordinates of the point 𝐵 where 𝐴𝐵 is the diameter of the circle.

b. 𝐶(2,1) also lies on the circle. Use coordinate geometry to verify that angle 𝐴𝐶𝐵 = 900

in the triangle ABC having vertices at A(-2,5), B(6,1) and C(-2,-3), find the length of the median from vertex B to side AC.

x=5^1/4 5^-1/4 y=5^1/4 - 5^-1/4 prove that 5(x² y²)²=144?

a. The points 𝐴,𝐵 and 𝐶 have co-ordinates (−1,2),(1,1) and (2,3) respectively. Sketch the triangle 𝐴𝐵𝐶 .By calculating the lengths of the sides of this triangle, determine if it is scalene, isosceles, or equilateral.

b. Find the distance 𝑀𝐵, where 𝑀 is the midpoint of 𝐴𝐶, and hence find the area of the triangle 𝐴𝐵𝐶.

a. The points 𝐴,𝐵 and 𝐶 have co-ordinates (−1,2),(1,1) and (2,3) respectively. Sketch the triangle 𝐴𝐵𝐶. By calculating the lengths of the sides of this triangle, determine if it is scalene, isosceles, or equilateral.

The line joining the point 𝐴 (4,6) 𝑡𝑜 𝐵 (𝑏,−3) has a gradient of 3. Find the value of 𝑏.

𝑃 and 𝑄 are the points (3,1) and (−2,−9) respectively. Calculate:

a. The distance 𝑃𝑄

b. The midpoint of the line joining 𝑃 to 𝑄

c. The gradient of the line 𝑃𝑄

d. The gradient of a line perpendicular to 𝑃𝑄